We give sufficient conditions for a discrete set of points in any dimensional real hyperbolic space to have positive anchored expansion. The first condition is an anchored bounded density property, ensuring not too many points can accumulate in large regions. The second is an anchored bounded vacancy condition, effectively ensuring there is not too much space left vacant by the points over large regions. These properties give as an easy corollary that stationary Poisson–Delaunay graphs have positive anchored expansion, as well as Delaunay graphs built from stationary determinantal point processes.

中文翻译：

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Delaunay 复形在实双曲空间和驻点过程中的锚定展开

我们给出了任何维实双曲空间中离散点集具有正锚定扩展的充分条件。第一个条件是锚定有界密度属性，确保不会在大区域中积累太多点。第二个是锚定有界空位条件，有效地确保大区域上的点不会留下太多空位。这些性质很容易推论，平稳 Poisson-Delaunay 图具有正锚定扩展，以及由平稳行列式点过程构建的 Delaunay 图。